Joe:
Welcome to the forum!
Take a soft bristle brush and sweep away as much of the dirt you can move. (like the archies do) and look closely around the body of the object for other markings.
You didn't say if it is attached to the rock in someway. If it is, take a LOT of compass readings from it; each claw, the base of the tail, the end of the tail, across the eyes, etc. Make a drawing of the object and strike lines on all reverences with compass headings shown. Use straight readings off of you compass so you can make the deviation corrections later.
Take ONE of your photos (the one with the tape measure in it would be good) and find an antiquities professor at a local college and ask his / her opinion on what it is and what it represents. If I'm not mistaken, there are some seriously TOUGH antiquities laws in Israel and if this is a really important find, in that area of interest, you'll want to know everything possible about what your legal position is. If you show that photo to a professor and tell him "a tourist" showed you the pix and you were curious as to it's meaning, maybe you can find out what you need to know, without putting yourself in an awkward situation.
If Romans were in the area, it MIGHT be connected to a cache since those folks were known to hide stuff for security. Look at all of the Roman caches found in England. Those Romans stole everything they could get their hands on when they "conquered" the Holy Lands.
